论文标题
从反射的Lévy过程到随机单调马尔可夫的过程，通过广义倒置和超模样
From reflected Lévy processes to stochastically monotone Markov processes via generalized inverses and supermodularity
论文作者
论文摘要
最近证明，反射lévy过程的固定版本的相关函数是非负，非插入和凸的。在文献的另一个分支中，可以确定从零开始反射过程的平均值是无负，无偏见和凹的。在本文中，通过将它们放置在共同的框架中，即这些结果扩展到了更一般的设置。实际上，我们考虑了一类更一般的随机单调马尔可夫过程，而不是反射的莱维过程。在此设置中，我们显示了与我们的马尔可夫过程的两个坐标的超模块函数相关的单调性结果，而上述单调性和凸/凹度的结果直接随之而来，但现在用于马尔可夫过程，而不仅仅是仅仅被认为是反射的莱维过程。此外，提供了瞬态情况的各种结果（当Markov过程不在平稳性的情况下）。所施加的条件是自然的，因为它们被各种经常使用的马尔可夫模型所满足，如一系列示例所示。
It was recently proven that the correlation function of the stationary version of a reflected Lévy process is nonnegative, nonincreasing and convex. In another branch of the literature it was established that the mean value of the reflected process starting from zero is nonnegative, nondecreasing and concave. In the present paper it is shown, by putting them in a common framework, that these results extend to substantially more general settings. Indeed, instead of reflected Lévy processes, we consider a class of more general stochastically monotone Markov processes. In this setup we show monotonicity results associated with a supermodular function of two coordinates of our Markov process, from which the above-mentioned monotonicity and convexity/concavity results directly follow, but now for the class of Markov processes considered rather than just reflected Lévy processes. In addition, various results for the transient case (when the Markov process is not in stationarity) are provided. The conditions imposed are natural, in that they are satisfied by various frequently used Markovian models, as illustrated by a series of examples.
